Research On The Solution Set Of Interval Linear Systems

The solution set of interval linear systems is the basis of interval optimization theory.So far,the research on the solution of interval linear equations and interval inequality systems is more mature,but the research on the solution of mixed interval systems is not much.Therefore,it is a significant subject to study the characteristics and structure of the solution of mixed interval systems.In the linear optimization problem,due to complicated circumstances,incomplete information and uncertainty of subjective thinking,often lead to some of the parameters in linear programming problem is not a determined value,namely the objective function and constraints are interval numbers.Therefore,it has important theoretical significance and practical value to study the comparison between the interval numbers and the ranking of the interval numbers.So far,there have been scholars from different angles to give different definitions to determine the size of the interval number.However,few scholars use the definition of the possibility to determine the equal relationship between interval numbers.This thesis is mainly divided into three research directions: hybrid interval equations recognition function of interval equal to the number of possible degree is defined and the corresponding properties and interval inequality system,and through the coefficient matrix and the right vector change interval linear systems of linear interval system correction.The main work of this thesis is as follows:The first chapter is the introduction part.Firstly,the research significance of the solution of interval linear systems is introduced,and the basic knowledge and the basic symbols of interval linear systems are summarized.Then,some basic solutions of interval linear equations and interval inequality systems are introduced,and the necessary and sufficient conditions are given.Then,it summarizes the research status and significance of the interval number.A preliminary introduction to the possibility of previous definitions by different angles is presented.Finally,the recognition function of interval linear system is proposed,and the research contents and structure of this paper are summarized.In the second chapter,the 64 different types of solutions of the mixed interval systems are discussed and the necessary and sufficient conditions for these solutions are given.First introduced the hybrid interval M.Hladik gives strong and weak solutions in the establishment of the necessary and sufficient condition,and then in a similar form given mixed interval system more general solution of sufficient and necessary conditions and the similar method is proved.The necessary and sufficient conditions for the establishment of 64 different types of solutions of the hybrid interval system are introduced.In the third chapter,it discusses the possibility of ranking interval numbers.In this thesis,the authors give the definition of different possible degrees from different angles,so as to determine the relationship between the size and the size of the interval number.And from different aspects to analyze the pros and cons.So far,the research about the possibility of interval number is used to compare the relationship between the interval numbers,and the research on the interval number is very few.To solve this problem,this thesis puts forward the definition of the equal probability of interval numbers,and gives some good mathematical properties.Finally,a concrete example is given,and the possibility of this chapter can be used to solve the practical linear programming problem with equality constraints.The fourth chapter introduces the recognition function of linear equations of interval previous definitions,based on a similar definition recognition function inequality of interval systems,and given interval system identification function for some basic properties,such as continuity,linear etc.In the end,the system is adjusted by changing the coefficient matrix and the right end of the internal linear system.In the fifth chapter,the main research results of this thesis are summarized,and the prospect of further research is put forward.